Question

A gift shop is going out of business. Prices for all items in
the store were assigned in July. Each month after that, the
price was 40% less than the price the previous month. If the
price of an item was d dollars for July, what was the price
for October?

(A) 0.128d
(B) 0.16d
(C) 0.2d
(D) 0.216d
(E) 0.64d

Answer 1

As said in the question it self the price of the items will be reduced by 40% after each month. The difference between the months of July and October are 3 
(i) the price in the month of July :
⇒ 40% of $100 is $40
(difference between $40 and $100)
⇒ $60
∴ cost of items in the month of July = $60 

(ii) the price in the month of August :
⇒ 40% of $60 is $24
(difference between $24 and $60) 
∴ cost of items in the month of August = $36 

(iii) the price in the month of September : 
⇒ 40% of $36 is 14.40 
(difference between $14.40 and $36) 
∴ cost of items in the month of September = $21.60

(iv) the price in the month of October :
for finding out the price we will try to do with the trial and error method by multiplying the given options with "100"
(A) 0.128 × 100 = 12.8
(B) 0.16 × 100 = 16
(C) 0.2 × 100 = 20
(D) 0.216 × 100 = 21.6
(E) 0.64 × 100 = 64 

⇒ option (D) is the correct option 

Answer 2

So, going according to the question

The prices were assigned in July. We have to find the price in October.

July
August
September
October

The price in July = d

So, price in October would be
60% of [60% of (60% of price in July)]

[60% because after taking out 40% the remaining would be 60% ; 100% - 40% = 60%]

That would be

60/100 × 60/100 × 60/100 × d

= 3/5 × 3/5 × 3/5 × d

= 27d/ 125

= 0.216d

So, the answer is (d) 0.216d